Alternate Image Processing Techniques

There are many other image processing techniques that can be employed within the SDO coding framework. Any process that accomplishes a coding step yielding the same or a similar result can be considered, especially if that new step is faster or more accurate. Many different types of techniques were considered

throughout the development of the code, but often times, a functional method was selected for simplicity and not necessarily optimization.

To illustrate, an example alteration is executed addressing the limb darkening correction step. The current code steps involve the addition of an inverted

correction image (derrived from the Eddington appriximation) to the grayscale sun in order to flatten out the intensity levels of the sun. This process is described in depth in Section 3.3.3.

An alternative way to complete this step would be to multiply a correction function into the grayscale image to achieve the flattening. The theory behind this relates to the concept of optical depth. The derivation of the Eddington relation (to the first order approximation) gives the intensity profile of the sun for varying angles of θ off from the center of the sun. This function is an approximation of the intensity drop visible on the photosphere, but if it is inverted and multiplied into the grayscale sun, all intensity drop off with angle should be corrected to the first order. This would be equivalent to having a uniform intensity and multiplying first by some intensity profile a to obtain the limb darkened sun (the starting image) and then multiplying by the ¹_a in order to re-scale the whole multiplicative factor to 1.

In practice, this method is simple enough to construct because the limb darkening function is already known to first order. Figure 45 shows the results of the multiplication of the inverse Eddington approximation with the gray sun image before any correction has been applied. Figure 46 shows the limb darkening

correction obtained through the addition method used currently in the code, and there is some clear difference on the limb of the sun.

Figure 45. The inverse of the Eddington approximation function is multiplied into the grayscale sun to correct for limb darkening.

Some differences are clear, including a faster drop off on the multiplied image near the very edge of the sun. In order to highlight these differences, the multiplied image is subtracted from the added image, shown in Figure 47.

The difference image shows some higher intensity near the edge of the sun, indicating that the added image yields higher pixel intensity in those regions. The

Figure 46. The inverse of the Eddington approximation function has been added to the grayscale sun in this case to correct for limb darkening. This is the method currently used by the SDO code.

intensity of spots in those regions looks to be visible as well, indicating that there will be a difference in the spot finding if the multiplication method is used. The correction may improve if the intensity correction function is found to a higher order. This may be a path for additional research, in addition to other image processing techniques that may be used to speed up the execution of the code.

Figure 47. The multiplication method for limb darkening correction is subtracted from the addition method used by the SDO code. The result proves to have higher pixel intensity near the edge of the sun.

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Vita

Second Lieutenant Gordon Spahr was born in Oakland, CA. After graduating from Acalanes High School in 2008, he was accepted to the United States Air Force Academy as part of the Class of 2012. Graduating with a Bachelor of Science Degree in Physics, he was commissioned into the United States Air Force from Cadet Squadron 34.

Lieutenant Spahr’s initial assignment upon commissioning was to the Air Force Institute of Technology at Wright Patterson AFB, OH. In fall of 2012, he entered the Applied Physics program to obtain a Master’s Degree, concentrating in Solar Physics and Space Weather. Upon graduation, Lieutenant Spahr will be assigned to the 47th Flying Training Wing for Specialized Undergraduate Pilot Training.

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